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Additional resources for Key Factors of Combustion: From Kinetics to Gas Dynamics
For this purpose at calculations under conditions of Fig. e. positive chain interaction was excluded. The results are shown in Fig. 7c. As is seen, the transition to chain-thermal mode occurs much later, than in Fig. 7a. It means that positive chain interaction facilitates the flammability of gas mixture. We will note also that under conditions of Fig. 7c at P = 5 Torr the stationary mode of flame propagation, as it would be expected, is missing: neither a non-thermal mode (k3 = 0), nor thermal one (low pressure) of flame propagation cannot be realized.
It should be noted (see above) that the steady-state non-thermal propagation of the flame (wave regime) must be considered with no regard for chain initiation reaction . It was also shown  that the role of linear chain branching is negligible (in view of the small value of k2 as compared with k1 and k3) to take it into account. However, it is evident that the rate of linear chain branching reaction cannot be neglected in the thermal ignition area. The characteristic scales as well as dimensionless variables and parameters of the process were chosen similar to Sect.
2 Propagation of Non-thermal Flame in the Low-Pressure … 23 limits of non-thermal flame propagation. If it was necessary to carry out long calculations, the following procedure was performed. The propagating wave occupied up to 50 nodes on the grid. When the wave approached the left border of calculation area and it was completely within the left 100 nodes on the grid (on the right, there were only zero values), the Yi values from the left half of a grid were transferred to the right half and the calculations were continued.
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